Hi Cliff, Thanks very much for providing your opinion too.
It was checked out by an Audi specialist who did confirm that it was the Dual-Mass flywheel. They've changed the whole clutch kit (for £750 including VAT and labour), and said to me afterwards that it was badly damaged inside, and I could have easily damaged the gearbox if I'd driven much further. Interesting - as apart from the shaking, there wasn't too nasty a noise from the engine like those I've seen on youtube videos where the DMF was failing badly.
Sadly, there is still a small, regular vibration (like a much reduced version of the initial problem) while idling. The garage assure me that it's ok, and that they suspect that it will diminish over time, and may be a result of some damage done while the DMF was failing... But also mentioned injectors as a possible cause... They've sent me away for now to keep an eye on it.
Will keep this updated with any further developments, but thanks again for the contributions gents.
Glen